TSTP Solution File: ALG428-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:32:42 EDT 2023

% Result   : Unsatisfiable 29.38s 13.53s
% Output   : CNFRefutation 29.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   77
% Syntax   : Number of formulae    :   90 (  11 unt;  70 typ;   0 def)
%            Number of atoms       :   36 (  15 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (  18   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   90 (  66   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :   55 (  53 usr;   2 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_Parity_Oeven__odd__class_Oeven > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_RealVector_Oreal__normed__algebra > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__comm__monoid__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_Divides_Osemiring__div > class_Divides_Oring__div > c_Polynomial_OpCons > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > c_Divides_Odiv__class_Omod > c_Polynomial_Odegree > c_HOL_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Suc > c_HOL_Ozero__class_Ozero > v_thesis____ > v_p > tc_nat > tc_Complex_Ocomplex

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_HOL_Ozero,type,
    class_HOL_Ozero: $i > $o ).

tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

tff(class_OrderedGroup_Ocancel__comm__monoid__add,type,
    class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring__0,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

tff(class_OrderedGroup_Oordered__ab__group__add,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Parity_Oeven__odd__class_Oeven,type,
    c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).

tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(class_Ring__and__Field_Oordered__semiring,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

tff(class_Ring__and__Field_Osemiring,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(class_Ring__and__Field_Oring,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(tc_Polynomial_Opoly,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(class_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(v_thesis____,type,
    v_thesis____: $o ).

tff(class_Ring__and__Field_Omult__zero,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

tff(class_OrderedGroup_Olordered__ab__group__add,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(class_OrderedGroup_Oab__semigroup__mult,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(class_Ring__and__Field_Ono__zero__divisors,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

tff(class_Ring__and__Field_Opordered__ring,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(class_Ring__and__Field_Oordered__ring__strict,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(class_Lattices_Oboolean__algebra,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(c_Orderings_Oord__class_Omin,type,
    c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).

tff(c_Suc,type,
    c_Suc: $i > $i ).

tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(class_Ring__and__Field_Ocomm__ring__1,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

tff(class_Ring__and__Field_Ofield,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(class_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

tff(class_OrderedGroup_Ocancel__semigroup__add,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(c_lessequals,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(tc_nat,type,
    tc_nat: $i ).

tff(c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(class_RealVector_Oreal__normed__algebra,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Ocomm__monoid__add,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(c_Orderings_Oord__class_Omax,type,
    c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

tff(class_Ring__and__Field_Oidom,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(class_OrderedGroup_Omonoid__add,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

tff(class_Ring__and__Field_Ocomm__ring,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

tff(class_Ring__and__Field_Oordered__semiring__strict,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

tff(c_HOL_Oplus__class_Oplus,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(c_HOL_Otimes__class_Otimes,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(tc_Complex_Ocomplex,type,
    tc_Complex_Ocomplex: $i ).

tff(c_HOL_Ozero__class_Ozero,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(c_Polynomial_OpCons,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Omult__mono1,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

tff(class_OrderedGroup_Oab__group__add,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(c_HOL_Ouminus__class_Ouminus,type,
    c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Ogroup__add,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(c_Polynomial_Odegree,type,
    c_Polynomial_Odegree: ( $i * $i ) > $i ).

tff(class_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(class_Ring__and__Field_Omult__mono,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(v_p,type,
    v_p: $i ).

tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

tff(c_HOL_Ominus__class_Ominus,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Opordered__ab__group__add,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(class_Ring__and__Field_Oordered__semidom,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(f_2300,axiom,
    ! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file(unknown,unknown) ).

tff(f_5335,axiom,
    class_Orderings_Olinorder(tc_nat),
    file(unknown,unknown) ).

tff(f_231,axiom,
    ! [T_a,V_y,V_x] :
      ( ~ class_Orderings_Olinorder(T_a)
      | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
      | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
      | ( V_x = V_y ) ),
    file(unknown,unknown) ).

tff(f_592,axiom,
    ! [V_n] :
      ( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    file(unknown,unknown) ).

tff(f_5283,axiom,
    ~ v_thesis____,
    file(unknown,unknown) ).

tff(f_5288,axiom,
    ! [V_x] :
      ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) )
      | v_thesis____ ),
    file(unknown,unknown) ).

tff(f_5281,axiom,
    c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
    file(unknown,unknown) ).

tff(c_640,plain,
    ! [V_n_960] : ~ c_HOL_Oord__class_Oless(V_n_960,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(cnfTransformation,[status(thm)],[f_2300]) ).

tff(c_1656,plain,
    class_Orderings_Olinorder(tc_nat),
    inference(cnfTransformation,[status(thm)],[f_5335]) ).

tff(c_58,plain,
    ! [V_y_87,V_x_88,T_a_86] :
      ( ( V_y_87 = V_x_88 )
      | c_HOL_Oord__class_Oless(V_x_88,V_y_87,T_a_86)
      | c_HOL_Oord__class_Oless(V_y_87,V_x_88,T_a_86)
      | ~ class_Orderings_Olinorder(T_a_86) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_50025,plain,
    ! [V_n_3403] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n_3403,tc_nat)
      | ( c_Suc(c_HOL_Ominus__class_Ominus(V_n_3403,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n_3403 ) ),
    inference(cnfTransformation,[status(thm)],[f_592]) ).

tff(c_1584,plain,
    ~ v_thesis____,
    inference(cnfTransformation,[status(thm)],[f_5283]) ).

tff(c_1586,plain,
    ! [V_x_2292] :
      ( v_thesis____
      | ( c_Suc(V_x_2292) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ),
    inference(cnfTransformation,[status(thm)],[f_5288]) ).

tff(c_1783,plain,
    ! [V_x_2292] : ( c_Suc(V_x_2292) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
    inference(negUnitSimplification,[status(thm)],[c_1584,c_1586]) ).

tff(c_74850,plain,
    ! [V_n_3668] :
      ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_n_3668 )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n_3668,tc_nat) ),
    inference(superposition,[status(thm),theory(equality)],[c_50025,c_1783]) ).

tff(c_74913,plain,
    ! [V_y_87] :
      ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_y_87 )
      | ( c_HOL_Ozero__class_Ozero(tc_nat) = V_y_87 )
      | c_HOL_Oord__class_Oless(V_y_87,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | ~ class_Orderings_Olinorder(tc_nat) ),
    inference(resolution,[status(thm)],[c_58,c_74850]) ).

tff(c_75021,plain,
    ! [V_y_87] :
      ( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_y_87 )
      | ( c_HOL_Ozero__class_Ozero(tc_nat) = V_y_87 )
      | c_HOL_Oord__class_Oless(V_y_87,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1656,c_74913]) ).

tff(c_75057,plain,
    c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(negUnitSimplification,[status(thm)],[c_640,c_75021]) ).

tff(c_1582,plain,
    c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(cnfTransformation,[status(thm)],[f_5281]) ).

tff(c_75062,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_75057,c_1582]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.32  % Computer : n032.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu Aug  3 20:18:51 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 29.38/13.53  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.38/13.53  
% 29.38/13.53  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.54/13.56  
% 29.54/13.56  Inference rules
% 29.54/13.56  ----------------------
% 29.54/13.56  #Ref     : 34
% 29.54/13.56  #Sup     : 16023
% 29.54/13.56  #Fact    : 10
% 29.54/13.56  #Define  : 0
% 29.54/13.56  #Split   : 7
% 29.54/13.56  #Chain   : 0
% 29.54/13.56  #Close   : 0
% 29.54/13.56  
% 29.54/13.56  Ordering : KBO
% 29.54/13.56  
% 29.54/13.56  Simplification rules
% 29.54/13.56  ----------------------
% 29.54/13.56  #Subsume      : 5389
% 29.54/13.56  #Demod        : 8737
% 29.54/13.56  #Tautology    : 4723
% 29.54/13.56  #SimpNegUnit  : 396
% 29.54/13.56  #BackRed      : 12
% 29.54/13.56  
% 29.54/13.56  #Partial instantiations: 0
% 29.54/13.56  #Strategies tried      : 1
% 29.54/13.56  
% 29.54/13.56  Timing (in seconds)
% 29.54/13.56  ----------------------
% 29.54/13.57  Preprocessing        : 1.60
% 29.54/13.57  Parsing              : 0.91
% 29.54/13.57  CNF conversion       : 0.13
% 29.54/13.57  Main loop            : 10.91
% 29.54/13.57  Inferencing          : 1.70
% 29.54/13.57  Reduction            : 5.50
% 29.54/13.57  Demodulation         : 4.08
% 29.54/13.57  BG Simplification    : 0.22
% 29.54/13.57  Subsumption          : 2.89
% 29.54/13.57  Abstraction          : 0.17
% 29.54/13.57  MUC search           : 0.00
% 29.54/13.57  Cooper               : 0.00
% 29.54/13.57  Total                : 12.56
% 29.54/13.57  Index Insertion      : 0.00
% 29.54/13.57  Index Deletion       : 0.00
% 29.54/13.57  Index Matching       : 0.00
% 29.54/13.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------